4.10. Evolution along the Hubble sequence and growth of the black hole

Non-axisymmetric instabilities like bars force the galaxies to evolve
towards large mass concentrations, large bulge-to-disk ratios, lower
gas content through consumption by star formation. This means
that a galaxy born as a late-type, will progressively evolve towards
early-types, with a somewhat chaotic path, from barred to unbarred, and
sometimes moving backwards, when the disk accretes mass. The gross
lines of this evolution are sketched in fig 14.

Figure 14. Cartoon of galaxy evolution
along the Hubble sequence.
A galaxy, with a small mass distributed mainly in a disk, without bulge
(late-type),
is unstable with respect to spiral and bar formation (steps 1 and 2).
The bar drives the gas towards the center, and the bulge is building up
(see in each frame the edge-on projection). When there is too much mass
concentrated in the center, the bar is destroyed (step 4), and the gas coming
from the outer parts, enrich the disk, and re-establish a larger disk
to bulge ratio. Later on (steps 5 and 6), another bar will form, when
the disk to bulge
ratio is favorable. A secondary bar (cf step 3) may help the primary
one to drive the mass towards the center. At the end, the galaxy may be
classified early-type.

To summarize this bar-driven evolution, and gather the main
features obtained through N-body simulations,
and supported by observations, it is interesting to test a toy model, in a
semi-analytical way, including:

- star formation, with a combination of
a quiescent rate, proportional to the gas
density, in a time scale of 3 Gyr, and
a bar-driven contribution, with a threshold
(Q < 1) and a rate equal to (1 - Q) / t*,
with t*, the star-formation time-scale (proportional
to the dynamical time-scale for gravitational instabilities).

Figure 15 displays some results of the toy
model (Combes, 2000).
The most striking feature is the self-regulation
of the stability parameter Q towards 1. Although the
galaxy initially starts almost completely gaseous, the gas
mass fraction soon stabilises to 10% of the total. Also
the mass of the central concentration (or black hole)
stabilises to a constant fraction of the bulge mass, as observed
(Magorrian et
al. 1998).

Figure 15. Model of periodic gas accretion
in a galaxy with star formation,
birth and death of bars, radial flows and black hole formation taken into
account: Top left Full line: gas mass versus time;
dash line: gas mass fraction. Top middle Full line: stellar
mass; dash lines: disk
stellar mass at top, and bottom bulge mass. Top right Full
line: total mass;
dash lines: total disk mass at top, and bottom bulge mass.
Bottom left Disk star formation rate versus time. Bottom middle
Toomre Q parameter. Bottom right Full line: mass of the central
black hole,
and dash line: mass ratio between the black hole and the bulge.